To answer this question, you need to understand the concept of the Pigeonhole Principle. The Pigeonhole Principle states that if you have more items than the number of containers, then at least one container must contain more than one item.
In this case, we have 12 black socks and 12 white socks, which totals 24 socks. To guarantee that we have a matching pair, we need to take out socks until we have more than 12 socks, as there are only 12 different colors (black and white).
Let's go through each option to determine the smallest number of socks you need to take out to be sure of having a matching pair:
Option A) 5 - If you take out 5 socks blindly, it is possible that you could have taken 3 black socks and 2 white socks, or vice versa. In this case, you do not have a matching pair yet.
Option B) 7 - If you take out 7 socks blindly, it is possible that you could have taken 4 black socks and 3 white socks, or vice versa. In this case, you do not have a matching pair yet.
Option C) 3 - If you take out 3 socks blindly, it is possible that you could have taken 2 black socks and 1 white sock, or vice versa. In this case, you still do not have a matching pair yet.
Option D) 1 - If you take out 1 sock blindly, regardless of the color, you cannot guarantee a matching pair. Therefore, this option is incorrect.
The correct answer is Option C) 3. This option is correct because by taking out 3 socks blindly, you can guarantee that you have a matching pair.